INVESTIGATION OF INFLECTION POINTS AS BRACE POINTS IN MULTI-SPAN PURLIN ROOF SYSTEMS

Transcription

1 INVESTIGATION OF INFLECTION POINTS AS BRACE POINTS IN MULTI-SPAN PURLIN ROOF SYSTEMS By Michael R. Bryant Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University In partial fulfillment of the requirements for the degree of MASTER OF SCIENCE In Civil Engineering APPROVED: T.M. Murray, Chairman W.S. Easterling T. E. Cousins June, 1999 Blacksburg, Virginia

2 Investigation of Inflection Points as Brace Points in Multi-Span Purlin Roof Systems by Michael R. Bryant Committee Chairman: Thomas M. Murray Civil Engineering (ABSTRACT) An experimental and analytical investigation was conducted to evaluate the behavior of inflection points as brace points in multi-span purlin roof systems. Seven tests were conducted using C and Z purlins attached to standing seam and through fastened panels. These tests were subjected to uniform gravity loading by means of a vacuum chamber. The experimental results were compared with analytical predictions based on the 1996 AISI Specifications with and without the inflection point considered a brace point. Finite element modeling of through fastened C and Z purlin tests were conducted and compared to experimental through fastened results. Conclusions were drawn on the status of the inflection point and on the design of multi-span purlin roof systems with current AISI Specifications. ii

3 Acknowledgements I would like to express my appreciation to my committee chairman, Dr. Thomas M. Murray. His guidance, advice, and patience over the course of this research was indispensable. I would also like to thank Dr. Samuel Easterling and Dr. Thomas Cousins for serving as committee members. I was very lucky to have help from many people while conducting my research. These people include: Mark Boorse, John Ryan, Tim Mays, Joe Howard, Ken Rux, Jim Webler, Marc Graper, Michelle Rambo-Roddenberry, and Emmett Sumner. I would like to extend my deepest gratitude to Brett Farmer and Dennis Huffman, first for their friendship and second for all their hard work in helping build my test set-ups. I would also like to thank Ann Crate for all her help. I would like to thank the many friends I have made here in Blacksburg. They have helped add many fond memories during my time here. Finally, I would like to thank the people most responsible for my success: my Mom, my Dad, and my Sister. They have given me their full support during my undergraduate and graduate work. Their generosity was more than anyone could possibly ask for. iii

4 TABLE OF CONTENTS ABSTRACT... LIST OF FIGURES... LIST OF TABLES... Page ii vi ix CHAPTER I. INTRODUCTION Introduction Literature Survey Doubly Symmetric Sections Singly and Point Symmetric Sections Scope of the Research Overview of Research II. TEST DETAILS Experimental Test Program Components of the Test Assemblies Test Setups III. EXPERIMENTAL RESULTS General Comments Tensile Test Results Summary of Test Results IV. ANALYTICAL RESULTS Background Z-Purlin Model C-Purlin Model iv

5 Chapter Page V. EVALUATION OF RESULTS Introduction Predicted and Measured Strains Predicted and Measured Purlin Spread Strength Evaluation Evaluation Assumptions AISI Specification Provisions Strength Comparisons Assuming the Inflection Point is not a Brace Point Strength Comparisons Assuming the Inflection Point is a Brace Point Strength Comparison Assuming a Fully Braced Cross-Section Summary of Test Results Comparison of Results VI. SUMMARY AND CONCLUSIONS Summary Conclusions Recommendations References APPENDIX A - TEST 1 Z - TF DATA APPENDIX B - TEST 2 Z - SS DATA APPENDIX C - TEST 3 C - SS DATA APPENDIX D - TEST 4 C - TF DATA APPENDIX E - I. P. TEST 1 Z - SS DATA APPENDIX F - I. P. TEST 2 Z - SS DATA APPENDIX G - I. P. TEST 3 Z - TF DATA v

6 LIST OF FIGURES Figure Page 1.1 Purlin Cross-Sections Typical Lap Configurations Typical Moment Diagram for Uniform Gravity Load Yura Inflection Point Investigation Through Fastened Panel Cross-Section Standing Seam Panel Cross-Section and Sliding Clip Virginia Tech Vacuum Chamber Ceco Building Systems Vacuum Chamber Plan View Ceco Building Systems Vacuum Chamber Section View Ceco Building Systems Vacuum Chamber Detail A Test 1 Z-TF and Test 2 Z-SS Span and Lap Configurations Test 3 C-SS and Test 4 C-TF Span and Lap Configurations I.P. Test 1 Z-SS, I.P. Test 2 Z-SS, and I.P. Test 3 Z-TF Span and Lap Configurations Potentiometer Support Configuration Spread Potentiometer locations in Test Bay Strain Gage Locations on Purlin Cross-Section Strain Gage Locations in Test Bay Strain Gage Locations in Test Bay Load vs. Strain Far Purlin Line vi

7 Figure Page 3.3 Potentiometer Locations in Test Bay Load vs. Spread Z TF Load vs. Spread Z SS Load vs. Spread C TF Load vs. Spread C SS Finite Element Cross-Section of Z Purlin Finite Element Side View of Z Purlin Boundary Conditions for Z Purlin Cross-Section Locations for Spread Measurements Load vs. Spread for Finite Element Z Purlin Model Locations for Strain Measurements Load vs. Strain for Finite Element Z Purlin Model Deflected Shape for Z-Purlin Model Finite Element Cross-Section of C Purlin Finite Element Side View of C Purlin Boundary Conditions for C Purlin Cross-Section Locations for Spread Measurements Load vs. Spread for Finite Element C Purlin Model Locations for Strain Measurements Load vs. Strain for Finite Element C Purlin Model Finite Element and Experimental Strain Results for Test 1 Z TF vii

8 Figure Page 5.2 Finite Element and Experimental Strain Results for Test 4 C TF Finite Element and Experimental Spread Results for Test 1 Z TF Finite Element and Experimental Spread Results for Test 4 C TF viii

9 LIST OF TABLES Table Page 2.1 Test Matrix Test Details Tensile Test Results Summary of Failure Loads and Locations Purlin Properties Strength Comparison (Inflection Point not as Brace Point) Strength Comparison (Inflection Point as Brace Point) Strength Comparison (Fully Braced Cross-Section) ix

10 CHAPTER I INTRODUCTION AND LITERATURE REVIEW 1.1 Introduction Purlin supported metal roofs have become a very popular choice for commercial buildings. The major reason behind the popularity is the advent of the standing seam system. Standing seam roof systems are aesthetically pleasing and have eliminated much of the leakage problems associated with metal roofs. Conventional through-fastened panel systems are still used in construction but require more maintenance over the life of the building. The majority of purlin supported roof systems employ the use of multi-span continuous purlins. The purlins may be continuous for only two spans or the purlins may be continuous across each span of the building. Purlins are rolled in many configurations, but the most widely used cross sections are stiffened Z and stiffened C shapes. These cross sections are shown in Figure 1.1. Continuity across the spans is achieved by lapping the purlins for a distance over each support. Typical lap configurations for Z- and C-purlins are shown in Figure 1.2. When considering simple spans subjected to uniform gravity loads, the entire purlin top flange is in compression and the entire bottom flange is in tension, this condition is called positive bending or positive moment. The top flange is fully braced when through fastened panel is used and partially braced with standing seam systems. When multiple continuous spans are subjected to uniform gravity loads, the conditions change. Regions near each internal 1

11 Z-PURLIN CROSS-SECTION C-PURLIN CROSS-SECTION Figure 1.1 Purlin Cross-Sections PURLIN LAP LAP SUPPORT SPAN SPAN SPAN Figure 1.2 Typical Lap Configurations 2

12 support experience negative moment. This means that the unsupported purlin bottom flange is in compression between the support and the inflection point, while the top flange that is attached to the decking is in tension. The inflection point on a continuous beam is the point where the moment is zero (moment actually switches from negative to positive at this point). The beam cross-section is subjected to negative moment between the internal support and the inflection point. The cross-section is subjected to positive moment between an inflection point and an exterior support or between inflection points in an internal span. A typical moment diagram is shown in Figure 1.3. A beam brace point is a location on the beam where the beam s tendency to twist and displace laterally is restrained. Inflection points have been assumed to act as brace points in continuous beams (Salmon and Johnson 1996) and in continuous purlin roof system design for some time (Murray and Elhouar 1994). Purlin supported roof systems are constructed of point-symmetric and singly-symmetric sections with their top flanges partially or fully braced by a sheeting diaphragm. Purlin roof systems are composed of beams that are considered continuous across multiple spans and subjected to uniform loads on all spans. This leads to inflection points that are much closer to the supports than at mid-span. Inflection points acting as brace points have been the subject of much discussion but little research has been conducted. An experimental and analytical investigation was conducted to evaluate the behavior of inflection points as brace points in multi-span purlin roof systems. Seven tests were conducted using C- and Z-purlins attached to standing seam and through fastened panel. These tests were subjected to uniform gravity loading by means of a vacuum chamber. The experimental results were compared with analytical predictions based on the 1996 AISI specification for the Design of Cold-Formed Steel Structural Members (Specifications 1996), hereafter referred to as the 1996 AISI Specifications, with and without the inflection point considered a brace point. 3

13 Load, W (plf) LAP LAP NEGATIVE MOMENT I. P. I. P. Lb POSITIVE MOMENT Figure 1.3 Typical Moment Diagram 1.2 Literature Review Much research has been performed on metal roofs supported by cold-formed purlins. The majority of the most recent research was concerned with determining the strength of standing seam roof systems. Little or no research has been conducted on cold-formed purlin inflection points and their status as brace points. Considerable research has been conducted on doubly symmetric shapes. Some of this research addresses inflection points and brace points. This literature review first covers research findings on hot-rolled doubly symmetric sections, followed by research on cold-formed C- and Z-purlins Doubly Symmetric Sections Beam and stability bracing has been studied by many over the years. Much of the most recent research has been conducted by Professor Joseph Yura at the University of Texas at Austin. Yura presents finite element and experimental results for various beam bracing conditions using hot rolled W-sections (W16X26) with span lengths of 20 ft. (Yura 1991, 1993). Yura concludes that restraining twist is the most critical component 4

14 of beam bracing. Yura also considers the case of a beam bent in double curvature by subjecting a 20 ft. simple span to equal but opposite end moments as shown in Figure 1.4. I. P. 20ft. Figure 1.4 Yura Inflection Point Investigation This causes an inflection point at mid-span and both flanges have portions that are in tension and in compression. Yura concluded that both top and bottom flanges must be braced (twist restrained) to gain more capacity over the unbraced case. If both flanges are braced at the midpoint, buckling moment increases nonlinearly as the brace stiffness increases up to the limit. Yura used a moment gradient factor of 1.75 to predict the critical moments for the W16X26 beam subjected to double curvature. The actual maximum moment was 25% higher than predicted, but brace stiffness must be increased by a factor of 4.3 to achieve the 25% capacity increase. The reason for the additional strength is because tension and compression exist in the same flange and this provides more warping resistance at mid-span. Yura points out that warping restraint isn t usually considered by design equations and this increased capacity should not be considered. Yura compares the double curvature case to a single point load applied at mid-span of an identical beam. The double curvature beam required a brace twice as stiff as the point load case in order to reach the same critical moment. Based on these observations Yura concludes that inflection points are not brace points and notes that bracing requirements at inflection points are greater than the bracing requirements for point loaded beams. Yura bases these conclusions on results from doubly symmetric sections and only considers simple spans with mid-span point loads or end moments. 5

15 The Guide to Stability Design Criteria for Metal Structures (Galambos 1998) addresses many topics related to beam buckling and beam bracing. Galambos sates that if a beam cross-section is subjected to a non-uniform moment, then the modifier known as C b can account for the effect of moment gradient in design equations. Galambos also states that it may be necessary to provide bracing to the compression (bottom) flange in negative moment regions to prevent lateral-torsional buckling. Johnson (1994) has published multiple papers on composite structures of steel and concrete. Information is provided on continuous beams and composite construction. The work presented is mainly for hot-rolled W sections shear connected to a concrete slab. Johnson states that near internal supports of continuous beams the bottom flange is compressed and the only lateral support for the bottom flange is provided by the flexible web. The concrete slab prevents twisting of the section as a whole. The bottom flange can only buckle if the web bends. This is referred to as distorstional lateral buckling. This type of buckle consists of one half-wave on each side of an internal support. This half-wave usually extends over most of the length of the negative moment region. Johnson states that this half-wave is not sinusoidal and the point of maximum lateral displacement is within two or three beam depths of the internal support. Johnson presents equations based on a U-frame model that can be used to predict critical moments for end span of a continuous beam. These equations apply to homogeneous doubly symmetric beam. The critical moment equations are also dependent on the torsional resistance provided by the concrete slab. Salmon and Johnson (1996) present a discussion on lateral buckling and continuous beams. Salmon and Johnson state that continuous beams have lateral end restraint moments that develop as a result of continuity over several spans. Some lateral restraint moment may result when adjacent spans are shorter, braced at closer intervals, or less severely loaded than the span considered. This lateral restraint may develop but should not be relied on in design because opposite unbraced spans might buckle in opposite directions eliminating any restraint present. 6

16 The inflection point has often been treated as a braced point when design equations did not provide for the effect of moment gradient (Salmon and Johnson 1996). Current ASD and LRFD equations include the moment gradient except for those equations used to determine a compact section (equations for L c and L p ). Salmon and Johnson state that one may wish to consider the inflection point as a possible braced point when determining L c or L p. The present opinion of Salmon and Johnson (1996) is that whenever moment gradient is included in a design equation, the inflection point should not be considered a brace point. However, when moment gradient is not included, in most cases the inflection point may be considered as a braced point. This is possible because of the torsional restraint provided by the floor or roof system attachments and the continuity at the support (point of maximum negative moment). The important factor in this assumption is the amount of torsional restraint provided by the floor system at the inflection point Singly- and Point Symmetric Sections The Guide to Stability Design Criteria for Metal Structures (Galambos 1998) includes a chapter discussing thin-walled metal construction. The chapter does not present principles exclusive to continuous beam design, but several of the important points will be summarized. First, the increased use of cold-formed steel members is reflected by the existence of design specifications in Australia, China, Europe, Japan, and North America. Moment capacity of thin-walled flexural members is governed by one or more of the following: yielding of material, local buckling of compression flange or web, and lateral buckling. It is stated that lateral buckling equations derived for I-beams can be used for channels and other singly symmetric shapes with reasonable accuracy. However, a Z-section with similar ratios will buckle laterally at lower stresses. To account for this the AISI specifications have added a conservative factor of 0.5 to the critical moment equations for Z-sections. Salmon and Johnson (1996) present a section discussing lateral buckling of channels, zees, monosymmetric I-shaped sections and tees. It is stated that the equations for lateral-torsional buckling of symmetric I-shaped may be applied to channels for 7

17 design purposes. Both the ASD and LRFD versions of the AISC Specifications have adopted this approach. It should be noted that an unconservative error of about 6 percent may exist in extreme cases when using this approach. Salmon and Johnson (1996) state that Z-sections are subject to unsymmetrical bending because the principle axis does not lie in the plane of loading. This leads to biaxial bending. The effect of biaxial bending on Z-sections was found to reduce the critical buckling moment by 5 to 10 percent. Unbraced Z-sections are rare and AISC does not address them. Salmon and Johnson recommend applying a factor of 0.5 to the critical moment equations for I-sections. Murray and Elhouar (1994) conducted a study that examined the approach to designing continuous Z- and C-purlins for gravity loading based on the 1986 AISI coldformed steel specifications. The paper begins by examining the assumptions commonly used when designing through fastened purlin roof systems. First constrained bending is assumed, this means that the purlin top flange is not free to rotate because it is directly fastened to sheeting. Purlins are lapped for a certain distance over the supports and the lapped portion is assumed to be fully continuous across the entire lap. The lapped region is assumed to have section properties and strengths equal to the sum of the section properties and strengths of the purlins that make up that lap. The region between the support and the end of the lap is assumed fully braced. The inflection point is considered a braced point. This is accounted for in design by considering the unbraced length for the negative moment region as the distance between the inflection point and the end of the lap. A moment gradient coefficient (C b ) is also incorporated into the moment capacity equations. Usually C b is taken as Murray and Elhouar collected data on multi-span continuous through fastened purlin tests subjected to gravity loading. These tests were conducted at various testing facilities. Each test was analyzed using the 1986 AISI Specifications and the assumptions previously mentioned to determine a predicted failure load without applying the ASD factors of safety. These values were then compared to the actual experimental failure loads. It was concluded that the assumptions as well as the 1986 AISI specifications were adequate for design. However, it should be noted that several of the 8

18 tests studied had experimental failure loads that were lower than the predicted values (unconservative predicted failure loads). Willis and Wallace (1991) presented a paper on the behavior of cold-formed steel purlins under gravity loading in Their study dealt with two aspects of Z- and C- purlin construction. The first aspect was the effect of fastener location on purlin capacity. The second aspect dealt with the width of compression flange lip stiffeners. This study reported analytical and experimental results on several single and three span tests. Willis and Wallace used two purlin lines spaced 5 ft. on center for each test. The purlins used were oriented with their top flanges opposed. The panel used in all tests was a standard through fastened panel that was attached to the purlin top flange with self-tapping screws with rubber washers. The only bracing applied to the bottom flange was at the supports where the cross-section was attached to anti-roll clips. The parameter that was intentionally varied was fastener location on the purlin top flange. The Willis and Wallace study presents predicted ultimate loads that were obtained by applying the provisions of the 1986 AISI Specifications to obtain an ASD allowable load and multiplying that value by 1.67 to remove the ASD factor of safety. The vertical deflection of each test is reported for a load that corresponds to the ASD allowable load. The other parameter that is reported is lateral movement or spread of the purlin bottom flange at the ASD allowable load. Spread and vertical deflection were both measured at the point of maximum vertical deflection for the corresponding test. Finally the predicted failure load is compared with the experimental failure load. The study concluded that Z- purlins were not noticeably affected by fastener location, but C-purlin capacity could be effected by as much as 10% by fastener location. The optimum fastener locations for C- purlins in near the stiffener lip. It is important to note that in this study, the capacities predicted by the 1986 AISI specification were near the experimental failure loads. Epstein, et al (1998) presented a study on the design and analysis assumptions for continuous cold-formed purlins. This report questions the validity of considering the entire lapped region as laterally braced. This study also questions the use of the inflection point as a braced point for determining the unbraced length for the negative 9

19 moment region. This study stresses that appropriate experimental testing is needed to verify or deny the assumptions used in continuous purlin design and that the suggestions presented by the authors should be verified experimentally. The only experimental research referenced by Epstein, et al was a study conducted by Murray and Elhouar (1994). Epstein, et al suggest that the Murray and Elhouar study did not support or verify the 1986 AISI Specifications. 1.3 Scope of Research One of the most important aspects of multi-span purlin roof system design is the unbraced length of the compression flange in the negative moment region. The 1986 AISI Specifications considers the inflection point as a brace point, therefore the unbraced length would be the distance between the end of the lap (which is considered braced) and the inflection point. A moment gradient coefficient (C b ) is also used in this procedure and incorporated into the lateral buckling equations. The 1996 AISI Specifications and the AISI Guide for Designing with Standing Seam Roof Panels (Fisher and La Boube 1997), hereafter referred to as the AISI Guide, recommend that the unbraced length still be considered the distance between the end of the lap and the inflection point but the inflection point is not considered braced and C b is taken as 1.0. The primary purpose of this research is to evaluate the accuracy of assuming the inflection point as a brace point when using current AISI specification procedures to predict the failure load of multiple span, multiple purlin line Z- and C-purlin supported through fastened and standing seam roof systems. Experimental testing was conducted involving multiple span Z- and C-purlins attached to standing seam and through fastened panel. Limited finite element modeling was performed and compared to the experimental results. 10

20 1.4 Overview Chapter II describes in detail the parameters of the experimental testing program. Purlin types and configurations as well as the types of panel and fasteners are discussed. Testing locations and measured parameters are also discussed. Chapter III presents all of the experimental results. Important observations are discussed. Chapter IV covers the finite element results. A simple model for both Z- and C- purlins is discussed. Results for a particular loading and boundary conditions are examined and compared to applicable experimental testing, as will be stresses at critical sections. Chapter V compares experimental results with the finite element modeling discussed in Chapter IV. Next, experimental results were evaluated using three different methods. The first approach is to assume the inflection point is not a brace point and predict a failure load based on those assumptions from the 1996 AISI Specifications. The second approach assumes the inflection point as a brace point and predicts failure loads based on this assumption. The third approach assumes a fully braced cross-section. Chapter VI presents conclusions based on all the information considered in this research. Recommendations are made concerning design procedures and possible further research. Appendices that contain summaries of all test data follow Chapter VI. 11

21 CHAPTER II TEST DETAILS 2.1 Experimental Test Program A series of seven tests were conducted. The first four tests were three span tests, whereas the last three were two span tests. The purpose was to determine if an inflection point is a brace point. Test components, procedures, and results are presented in the following sections. The test designations for these experiments are identified as Test # X-YY. Where # notes the chronological order of the test, and X could be Z for a Z-purlin or C for a C-purlin. The YY is used to denote the type of decking used, TF for through fastened panel or SS for standing seam panel. Tests 1 to 4 were conducted at Virginia Tech and I. P. Tests 1, 2, and 3 were conducted at Ceco Building Systems, Columbus, Mississippi. 2.2 Components of the Test Assemblies Manufacturers belonging to the Metal Building Manufactures Association (MBMA) supplied components used in the testing program. All standing seam tests used the same pan type panel and clips. Both three span through fastened tests used the same through fastened panel, whereas the two span test used a different through fastened panel. Table 2.1 shows the different test configurations used. Purlins. Both Z and C purlins were used in the tests. Actual properties such as depth, thickness, flange and stiffener length varied with each test. Measured purlin dimensions can be found in Appendix A through Appendix G. Tensile coupon tests were conducted from material taken from the web of representative purlins for each test. 12

22 Table 2.1 Test Matrix Test Designation Purlin Type Depth (in.) Panel Type Spans (ft.) Purlin Orientation Test 1 Z-TF Z 8 Through Fastened Test 2 Z-SS Z 10 Standing Seam Test 3 C-SS C 10 Standing Seam Test 4 C-TF C 8 Through Fastened 25, 23 25, Opposed Opposed Opposed Opposed I. P. Test 1 Z-SS I. P. Test 2 Z-SS I. P. Test 3 Z-TF Z 8.5 Standing Seam Z 8.5 Standing Seam Z 8.5 Through Fastened 30 Opposed 30 Opposed 30 Opposed Panels. The panels used in the tests were of three basic configurations. The first is a standard through fastened panel shown in Figure 2.1. The second configuration is a standing seam pan type panel with sliding clips shown in Figure 2.2. Finally the third 13

23 configuration uses the standing seam panel as a through-fastened panel with screws located near each seam or rib. SELF-TAPPING SCREW THROUGH FASTENED PANEL PURLIN Figure 2.1 Through Fastened Panel SLIDING CLIP STANDING SEAM PANEL Figure 2.2 Standing Seam Panel and Sliding clip Standing Seam Panel Clips. The standing seam clips used in testing were called high clips. These clips required a Styrofoam block be used between the pan type panel and the purlin top flange. The clips were attached to the purlin top flange using standard self-tapping screws supplied by the metal building manufacturer. Bracing. The rafters were the only location were bracing was provided. For the tests using Z-purlins, anti-roll clips were placed at each rafter support for both purlin lines. The bottom flanges of the purlins were also directly bolted to the rafters. For tests using C-purlins, anti-roll clips were placed only at the exterior support rafters. The bottom flanges of the purlins were also bolted directly to the rafters. 14

24 Tests I. P. Test 1, 2, and, 3 used anti-roll clips at each rafter support for both purlin lines. Test I. P. Test 2 Z-SS also had a brace attached between the purlin lines. The brace was attached at the theoretical inflection point. 2.3 Test Setups All tests were subjected to gravity loading. The gravity load was simulated with the use of a vacuum chamber. The vacuum chamber provides an airtight space around the test setup. Air is pumped out of the chamber with one or more vacuum pumps. This causes a negative differential pressure in the chamber. In essence the surrounding atmospheric pressure loads the test specimens. Tests were conducted in two locations, at the Virginia Tech Structures and Materials Research Laboratory, and at the Ceco Building Systems Research Laboratory in Columbus, Mississippi. The Virginia Tech vacuum chamber consisted of a box 8ft. x 78 ft. x 3 ft. The chamber is constructed from 3 ft. x 8 ft. galvanized steel panels. The joints between panels and between the panel and floor are sealed with caulk. Bulkhead panels can be inserted in the chamber to shorten the chamber when the entire length is not required. A plan view of the Virginia Tech vacuum chamber is shown in Figure 2.3. The Ceco Building Systems chamber consisted of a box ft. x 92 ft. x 3.83 ft. The Ceco chamber is constructed from two built-up I-sections stacked on each other and welded into place. The I-sections are sealed to the floor with caulk. Bulkhead panels can be inserted into the chamber to shorten the chamber to the required length. The Ceco chamber uses two additional purlin lines to reduce the width of the chamber to 8.5 ft. as shown in Figure 2.4 through Figure

25 5 25 PURLIN LINES 25 SUPPORTS 23 Figure 2.3 Virginia Tech Vacuum Chamber 16

26 LEGEND: ROTARY BLOWER WITH "U" TUBE MANOMETER FLEXIBLE HOSE SUPPORT FOR TEST MEMBER TEST MEMBER FILL-IN MEMBER ANTI- ROLL CLIP (CL203) 2 1/4" X 2 1/4" C C 10-7" 1-0 1/2" 1-9" A 5-0" B 1-9" 1-0 1/2" B-1 FACE OF END PLATE 1-0" 30-0" A-1 A-2 X B " 2-0" BULKHEAD FACE OF END PLATE " (NOT TO SCALE) Figure 2.4 Ceco Vacuum Chamber 10-2" (BETWEEN TEST BOX FLANGES) L 7-0" (PANEL LENGTH) 2 1/2"C 10" 9" 1-0" 5-0" 1-0" 9" PURLIN PANEL 10" C L2 1/2" DETAIL "A" 1-11" 3-10" 1-11" 3-0 1/2" FLANGES 5" ANTI-ROLL CLIP (CL203) W6X9 SUPPORT BEAM COLUMN PURLIN (2) 1/2"Ø A307 BOLTS W14X30 SUPPORT BEAM W6X9 TIE DOWN BEAM W6X9 SUPPORT BEAM COLUMN ANTI-ROLL CLIP (CL203) 5" FLANGES (2) 1/2"Ø A325 BOLTS (2) 1/2"Ø A325 BOLTS SIDE OF TEST BOX C L PLATE 5/8" X 8" X 1'-0 1/2" W/(4) 3/4"Ø EXPANSION ANCHORS 10-7" C L FIN. FLOOR (CONC. SLAB) Figure 2.5 Ceco Chamber Cross-Section 17

27 PANEL 9" 10" TEST BOX FLANGE POLYETHYLENE (6 MIL) CL 2 1/2" CONTINUOUS L2" X 2" X 1/8" "C" CLAMP (AS REQ D) 1" X 1" X DOUBLE 24 GA. ANGLE (NORTH AND SOUTH SIDE) ONE FASTENER EACH SIDE OF RIB FILL-IN PURLIN RESTRAINTS 8-1/2 Z88 FILL-IN PURLINS TYPICAL AT NORTH AND SOUTH SIDE Figure 2.6 Ceco Chamber Edge Detail A The configuration to be tested was then constructed inside the chamber. The top of the chamber was sealed with a sheet of polyethylene (6 mil thick). At Virginia Tech the air was removed from the chamber using a main vacuum pump and four auxiliary shop-type vacuum pumps. The Ceco tests used only one main vacuum pump to remove air from the chamber. All tests consisted of two purlin lines spaced 5 ft. on center. The purlin flanges were facing in the opposite direction for all tests. The panel used for all testing was 7 ft. wide. This allowed for a 1-ft. overhang from the centerline of the web of each purlin. All standing seam tests used sliding clips that were attached to the purlin with selfdrilling screws. The through-fastened panel was attached directly to the purlin with selfdrilling screws. The three span tests had varying parameters. The tests with Z-purlins had the span lengths of 25 ft., 25 ft., and 23 ft. The test bay with all instrumentation had a span length of 25 ft. while the opposite exterior bay was shortened to 23 ft. Lap splices at each interior support for the three span Z-purlin tests extended 1 ft. over each side of the support for a total lap length of 2 ft. The tests with C-purlins had a test span of 24.5 ft., a 18

28 middle bay with a span of 25 ft., and an end span of 23 ft. This was done to help ensure that failure occurred in the test bay. The lap splices at each interior support for the three span C-purlin tests extended 1 ft. in the direction of the exterior support and 2 ft. into the middle bay for a total lap length of 3 ft. Three two span tests were conducted. All span lengths were 30 ft. All two span tests used 8.5 in. deep Z-purlins. Two of the tests were conducted using standing seam panel, while the third used a through-fastened panel. The lap splice at the interior support of the two span tests extended 1.5 ft. beyond each support for a total lap length of 3 ft. Details of the test parameters are given in Table 2.2 and in Figure 2.7 through Figure 2.9. Data was collected electronically at Virginia Tech for the three span tests using a personal computer based data acquisition system. The two span tests that were conducted at Ceco Building Systems used manual data collection. The gravity loadings for tests at both locations were measured using U-tube manometers. The manometers have an accuracy of 0.1 in. of water. One inch of water is equivalent to about 5.2 psf. Vertical displacement transducers were used at Virginia Tech to measure maximum vertical deflections in the test bay. Vertical deflection was measured at Ceco building systems using a surveyor s level to read a scale that was placed over the theoretical point of maximum deflection. Measurements were taken for both purlins in the test bay of each test. No Measurements were taken in non-test bays. Lateral displacement of the test bay was measured for the three span standing seam tests. A vertical displacement transducer was used with a pulley system that allows the actual lateral movement to be calculated. This value was small because of the opposite orientation of the purlins. Spread of the test purlins was measured using potentiometers. Spread refers to the roll or lateral displacement measured approximately two inches above the purlin bottom flange with respect to the purlin top flange. The potentiometers were placed at the location of maximum moment and 1 ft. away from the calculated inflection point on both sides. The potentiometers were suspended from cold-formed angles that span across 19

29 the purlin lines in such a manner that they did not provided any additional bracing between the purlin lines as shown in Figure 2.10 and Figure The potentiometers measured the spread of the purlin at about two inches above the purlin bottom flange. Finally, tests conducted at Virginia Tech had strain gages placed on the top and bottom surface of the purlin bottom flange. This was done to find the location of the true inflection point. Ten gages were placed on each test purlin. They were located at the calculated inflection point, and 6 in., and 12 in. on each side of the calculated inflection point. The location of the inflection point was calculated using a non-prismatic stiffness analysis. Figure 2.12 and Figure 2.13 show typical strain gage locations. 20

30 Table 2.2 Test Details TEST # PURLIN TYPE SPANS Test 1 Z-TF 8 in. Z Test Bay: 25 ft. Middle Bay: 25 ft. End Bay: 23 ft. Test 2 Z-SS 10 in. Z Test Bay: 25 ft. Middle Bay: 25 ft. End Bay: 23 ft. Test 3 C-SS 10 in. C Test Bay: 24.5 ft. Middle Bay: 25 ft. End Bay: 23 ft. Test 4 C-TF 8 in. C Test Bay: 24.5 ft. Middle Bay: 25 ft. End Bay: 23 ft. I. P. Test in. Z Test Bay: 30 ft. Z-SS End Bay: 30 ft. I. P. Test in. Z Test Bay: 30 ft. Z-SS End Bay: 30 ft. I. P. Test in. Z Test Bay: 30 ft. Z-TF End Bay: 30 ft. TOTAL LAP LAP LENGTH INTO TEST BAY PANEL TYPE 2 ft. 1 ft. Through Fastened 2 ft. 1 ft. Standing Seam 3 ft. 1 ft. Standing Seam 3 ft. 1 ft. Through Fastened 3 ft. 1.5 ft. Standing Seam 3 ft. 1.5 ft. Standing Seam 3 ft. 1.5 ft. Through Fastened 21

31 TOTAL LAP LENGTH 2 2 TEST BAY MIDDLE BAY END BAY LAP EXTENSION INTO TEST BAY Figure 2.7 Test 1 Z TF & Test 2 Z SS TOTAL LAP LENGTH 3 3 TEST BAY MIDDLE BAY END BAY LAP EXTENSION INTO TEST BAY " Figure 2.8 Test 3 C SS & Test 4 C TF TEST BAY TOTAL LAP LENGTH 3 END BAY LAP EXTENSION INTO TEST BAY 1-6" Figure 2.9 I. P. Test 1, 2, and 3 22

32 SCREW FASTENER FASTENED END MOVES WITH PURLIN COLD-FORMED SUPPORT IS FREE TO SLIDE ACROSS TOP OF PURLIN COLD-FORMED SPPORT ANGLE POTENTIOMETER POSITIVE SPREAD DIRECTION Figure 2.10 Potentiometer Support Configuration Figure 2.11 Spread Potentiometer Support Locations in Test Bay 23

33 STRAIN GAGE LOCATIONS STRAIN GAGE LOCATIONS Figure 2.12 Z- and C-Purlin Strain Gage Locations Figure 2.13 Strain Gage Locations in Test Bay 24

34 CHAPTER III EXPERIMENTAL RESULTS 3.1 General Comments Individual results for each test are found in Appendices A through G. Each set of results includes a test summary sheet, measured purlin dimensions, section properties, flexural strength, purlin arrangement within each test, tensile coupon results, and results from a stiffness analysis. Each test appendix also includes individual data, plots of load versus deflection, load versus strain, load versus purlin spread, and flexural strength based on the assumption that the inflection point is a brace point and based on the assumption that the inflection point is not a brace point. A commercial software program was used to perform a non-prismatic stiffness analysis of the each test configuration. A non-prismatic analysis is needed because of the overlap of the purlins. The lapped region is stiffer and therefore attracts more moment. The models were built with actual section properties and loaded with a uniform load of 100 pounds per foot. Moments and shears from critical locations were then recorded for this loading, and were later scaled for other loadings. The stiffness models were also used to calculate locations of maximum moment, maximum deflection, and to calculate the location of the inflection point about which measurements were made. 25

35 3.2 Tensile Test Results At least one standard ASTM coupon was cut and machined from the undamaged web of a failed purlin from each test. The coupons were then tested according to ASTM loading procedures; where more than one coupon was tested, average values are reported. A summary of tensile test results is in Table 3.1. Table 3.1 Summary of Tensile Test Results Identification Thickness (in.) Width (in.) Yield Stress (ksi) Tensile Strength (ksi) Elongation % Test 1 Z-TF Test 2 Z-SS Test 3 C-SS Test 4 C-TF I.P. Test 1 Z-SS I.P. Test 2 Z-SS I.P. Test 3 Z-TF

36 3.3 Summary of Testing Results A summary of the failure loads and failure locations is given in Table 3.2. Two types of failure were observed in these tests. First was inelastic and local buckling near the face of the lap in the negative moment region of the test bay. The second type was local buckling of the compression flange, stiffener, and web near the location of maximum positive moment in the test bay. The failure load shown in Table 3.2 is the applied load in pounds per linear foot; the self-weight of the system was added later for analysis and comparison purposes. TABLE 3.2 Summary of Failure Loads and Locations Identification Number Applied Load at Failure Location of Spans Failure (plf) Test 1 Z-TF Negative Region* Test 2 Z-SS Positive Region Test 3 C-SS Positive Region Test 4 C-TF Negative Region* I. P. Test 1 Z-SS Positive Region I. P. Test 2 Z-SS Positive Region I. P. Test 3 Z-TF Negative Region* * Local buckling immediately outside of the lapped portion of the purlin in the exterior span. 27

37 As shown in Figure 3.1, the strain gage at position 8 is located at the calculated inflection point, Figure 3.2 shows that the strain at this location remains very low throughout the test demonstrating that the method used to calculate the inflection point is adequate. Figure 3.2 is typical for all tests that were strain gaged. Other plots of load versus strain can be found in the appendices. Figure 3.3 again shows the potentiometer locations for measuring purlin spread. Spread was measured at 1 ft. inside the calculated inflection point (negative moment region) and 1 ft. outside the inflection point (positive moment region). The spread was also measured at the location of maximum moment for all tests except Test 1 Z-TF. Figure 3.4 shows a plot of load versus spread for a typical through-fastened Z-purlin test. Figure 3.5 shows typical spread of a standing seam Z-purlin test. Figure 3.6 shows the typical behavior of a through-fastened C-purlin test and Figure 3.7 shows a typical standing seam C-purlin test. It was expected that very little movement would occur at an inflection point. It was hypothesized that out-of-plane double curvature might be exhibited near the inflection point, especially in the Z-purlin tests. The major reason for expecting this behavior was because of the conditions at the inflection point and the properties of the purlin cross-section. Negative moment is present between the interior support and the inflection point, while positive moment is present between the inflection point and the exterior support. The principle axis of a Z cross-section is inclined to the plane of loading This would seem to lead to the section wanting to rotate in one direction on one 28

38 I. P. FAR PURLIN STRAIN GAGE POSITIONS STRAIN GAGE POSITIONS NEAR PURLIN INTERIOR SUPPORT TEST BAY EXTERIOR SUPPORT Figure 3.1 Strain Gage Locations 300 Position Load (plf) Position 6 Position 7 Position 8 Position 9 Position Strain (ue) Figure 3.2 Load vs. Strain Far Purlin Line 29

39 side of the inflection point and another direction on the other side of the inflection point. The actual behavior was somewhat different. As shown in the figures of this chapter and in the appendices, the inflection point did not remain stationary in any test conducted. In general, the inflection point rolled inward for the tests using Z-purlins and outward for tests using C-purlins. The values of spread were small in all cases compared to the spread at maximum moment. It should be noted that the spreads of the Z-purlins were much less that the C-purlin spread. Test data and plots for each test can be found in appendices A through G. FAR PURLIN I. P. MAXIMUM MOMENT 1 1 PT 6 PT 4 MMFAR PT 5 PT 3 MMNEAR NEAR PURLIN INTERIOR SUPPORT TEST BAY EXTERIOR SUPPORT Figure 3.3 Potentiometer Locations 30

40 350 PT 5 PT 3 PT 4 PT Load (plf) PT 3 PT 4 PT 5 PT Spread (in.) Figure 3.4 Z-TF Load vs. Spread 160 PT 3 PT 5 MMFar PT Load (plf) PT 6 MMNear PT 3 PT 4 PT 5 PT 6 MMNear MMFar Spread (in.) Figure 3.5 Z SS Load vs. Spread 31

41 MMFar PT 6 PT 4 PT 5 PT Load (plf) 150 MMNear PT 3 PT 4 PT 5 PT 6 MMNear MMFar Spread (in.) Figure 3.6 C TF Load vs. Spread 250 PT 3 PT 4 PT 5 PT 6 MMFar MMNear 200 Load (plf) PT 3 PT 4 PT 5 PT 6 MMNear MMFar Spread (in.) Figure 3.7 C SS Load vs. Spread 32

42 CHAPTER IV ANALYTICAL RESULTS 4.1 Background Analytical studies were made of Z- and C-purlins lines using the finite element method. The purpose of the modeling was to determine if the experimental behavior of the purlin cross-section could be adequately modeled using simple procedures, therefore, the modeling is restricted to through fastened panel. It is possible to model the conditions of standing seam panel, but the uncertainty in the boundary conditions present at the panel/clip/purlin interface are beyond the scope of this research. Finite element modeling was done using the commercial finite element program Ansys 5.4 (Ansys 1996). The program has complete three-dimensional capabilities and is capable of modeling much more complex problems than required by this study. All modeling used four node shell elements with six degrees of freedom at each node. The shell elements were capable of transmitting flexural forces. These elements basically behaved like actual plates. These elements were chosen because of their ability to model three-dimensional behavior as well as their ability to properly model the large aspect ratios needed with modeling purlin lines. The aspect ratio is large because typical purlin cross-sections have depths of 8 to 10 in., flanges that are 2 to 4 in. wide with a thickness of 0.1 in. or less. The length of the purlin may be 20 to 40 ft. Certain types of elements require aspect ratios that leave the elements nearly square, this would required 2 to 3 times more elements than with the shell elements. 4.2 Z-Purlin Model The Z-purlin model was created to model the conditions of Test 1 Z-TF. When viewing the end of the purlin cross-section, the Y-axis is vertical, the X-axis is horizontal, and the Z-axis is into the page. The purlin cross-section is shown in Figure 4.1 with node locations and global axes shown. Figure 4.2 shows the length of the purlin in the Z direction. The Z-purlin model contains 2,800 elements and 17,700 degrees of freedom. 33

43 The modeling of the purlin lap required special consideration. The lap region has a thickness equal to the thickness of both purlins that are a part of the lap. In the case of Test 1 Z-TF a thickness of 0.2 inches was used. This translates to twice the thickness and twice the stiffness if the lap acts together as a unit. In actuality, the lap is connected by a specified number of bolts. The most accurate model would model the lap as two separate purlins bolted together at specified locations. However, the AISI Guide design models assume that the lap acts as one unit. Therefore, the lap was modeled as one continuous cross-section with twice the stiffness of one purlin. The lap region stiffness can be increased by increasing the thickness of the elements or by increasing the modulus of elasticity. Both properties were easy to modify and produced nearly identical results. The results presented in this study were obtained by doubling the thickness of the elements in the lapped region of the model. The required boundary conditions also required special considerations. At the supports, translations in the X and Y directions were restricted at locations that corresponded to the anti-roll clips as shown in Figure 4.3. These locations were allowed to rotate about the X-axis to simulate a pinned support condition. One end of the model 34

44 Y NODE SHELL ELEMENT Z GLOBAL AXES X Figure 4.1 Z Model Cross-Section NODES SHELL ELEMENTS Figure 4.2 Z Model Side View LOAD LOCATION Y DIRECTION RESTRAINED X DIRECTION RESTRAINED NODE SYMBOL Figure 4.3 Boundary Conditions at Supports 35

45 needed to have translation restricted in the Z direction to make the model stable. The boundary conditions of the purlin top flange required special consideration. The purlin top flange was fixed in the X direction at the intersection of the purlin top flange and web. These are the conditions provided by through-fastened panel. The purlin lateral movement or spread could be greatly effected by the location of load application. The uniform line load was placed one-third of the flange width away from the purlin web. Note that if load were transferred to the purlin top flange based on stiffness, the resultant of that distribution would coincide with the load location used in this model. Figure 4.3 shows the final boundary conditions and load location used for the model. Lateral or spread movement of the purlins at the locations shown in Figure 4.4 is plotted in Figure 4.5. The negative values imply movement of the purlin bottom flange to the left for the orientation shown in Figure 4.1. As with the experimental results, movement is greatest in the positive moment side of the inflection point and the entire area moves to the left. Loads versus strain at the locations shown in Figure 4.6 are plotted in Figure 4.7. Finally, Figure 4.8 shows the deflected shape of the bottom flange of the Z-purlin model. The values plotted in Figure 4.8 represent the lateral movement of the bottom flange at the intersection with the purlin web as you move along the length of the purlin. 36